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A mixed method for axisymmetric div-curl systems

Authors: Dylan M. Copeland, Jayadeep Gopalakrishnan and Joseph E. Pasciak
Journal: Math. Comp. 77 (2008), 1941-1965
MSC (2000): Primary 65F10, 65N30, 78M10, 74G15, 78A30, 35Q60
Published electronically: March 10, 2008
MathSciNet review: 2429870
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Abstract: We present a mixed method for a three-dimensional axisymmetric div-curl system reduced to a two-dimensional computational domain via cylindrical coordinates. We show that when the meridian axisymmetric Maxwell problem is approximated by a mixed method using the lowest order elements (for the vector variable) and linear elements (for the Lagrange multiplier), one obtains optimal error estimates in certain weighted Sobolev norms. The main ingredient of the analysis is a sequence of projectors in the weighted norms satisfying some commutativity properties.

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Additional Information

Dylan M. Copeland
Affiliation: Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria

Jayadeep Gopalakrishnan
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611–8105

Joseph E. Pasciak
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843

Keywords: Mixed methods, Nedelec elements, axisymmetry, Maxwell's equations, div-curl systems, magnetostatics
Received by editor(s): March 30, 2007
Received by editor(s) in revised form: August 29, 2007
Published electronically: March 10, 2008
Additional Notes: This work was supported in part by the National Science Foundation through grants DMS-0713833, SCREMS-0619080, DMS-0311902, and DMS-0609544.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.